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These are replies submitted by DGromov

@John Fredsted , many thanks! This is what I was after.


@Torre , thank you! Actually I thought about having something like this:

 [[aX+bY,cZ],[cY,bX+cZ]] = ac^2b [[X,Z],[Y,X]]+c^2b^2 [[Y,Z],[Y,X]]+ac^3 [[X,Z],[Y,Z]]

(this particular example is not very illustrative, though. There could be also some terms cancelled due to Jacobi identity)

I could get this by defining XY=[X,Y], XXY=[X,[X,Y]] etc, but then I'd need to set some high order brackets to 0 to close the system. I'm also affraid that defining all possible brackets up to, say, 4th order would be quite tedious...

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